LMFDB - Embedded newform 200.6.f.b.149.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(149,200)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 $ x^20 - 2x^19 - 17x^18 + 78x^17 + 253x^16 - 884x^15 + 2396x^14 + 19376x^13 - 109104x^12 - 96128x^11 + 3580672x^10 - 1538048x^9 - 27930624x^8 + 79364096x^7 + 157024256x^6 - 926941184x^5 + 4244635648x^4 + 20937965568x^3 - 73014444032x^2 - 137438953472*x + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{4}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.8
Root			$3.72553 - 1.45618i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.6.f.b.149.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.26935 + 5.18171i) q^{2} -10.8240 q^{3} +(-21.7001 - 23.5182i) q^{4} +(24.5634 - 56.0868i) q^{6} +163.706i q^{7} +(171.109 - 59.0729i) q^{8} -125.841 q^{9} +O(q^{10})$	\(q+(-2.26935 + 5.18171i) q^{2} -10.8240 q^{3} +(-21.7001 - 23.5182i) q^{4} +(24.5634 - 56.0868i) q^{6} +163.706i q^{7} +(171.109 - 59.0729i) q^{8} -125.841 q^{9} -321.520i q^{11} +(234.883 + 254.561i) q^{12} -128.246 q^{13} +(-848.277 - 371.506i) q^{14} +(-82.2074 + 1020.69i) q^{16} -2110.72i q^{17} +(285.576 - 652.070i) q^{18} -1454.37i q^{19} -1771.96i q^{21} +(1666.02 + 729.641i) q^{22} +1231.18i q^{23} +(-1852.09 + 639.406i) q^{24} +(291.033 - 664.531i) q^{26} +3992.34 q^{27} +(3850.07 - 3552.45i) q^{28} +4073.19i q^{29} -3956.03 q^{31} +(-5102.38 - 2742.28i) q^{32} +3480.14i q^{33} +(10937.1 + 4789.95i) q^{34} +(2730.76 + 2959.54i) q^{36} +10656.6 q^{37} +(7536.11 + 3300.46i) q^{38} +1388.13 q^{39} -5907.19 q^{41} +(9181.76 + 4021.18i) q^{42} +16439.6 q^{43} +(-7561.57 + 6977.04i) q^{44} +(-6379.59 - 2793.96i) q^{46} +23238.8i q^{47} +(889.814 - 11048.0i) q^{48} -9992.68 q^{49} +22846.5i q^{51} +(2782.95 + 3016.10i) q^{52} -30634.0 q^{53} +(-9059.99 + 20687.1i) q^{54} +(9670.60 + 28011.6i) q^{56} +15742.1i q^{57} +(-21106.1 - 9243.47i) q^{58} -25262.4i q^{59} +39115.5i q^{61} +(8977.61 - 20499.0i) q^{62} -20600.9i q^{63} +(25788.8 - 20215.9i) q^{64} +(-18033.1 - 7897.64i) q^{66} +20894.5 q^{67} +(-49640.3 + 45803.0i) q^{68} -13326.3i q^{69} +13889.1 q^{71} +(-21532.5 + 7433.78i) q^{72} +43451.2i q^{73} +(-24183.6 + 55219.6i) q^{74} +(-34204.1 + 31560.0i) q^{76} +52634.8 q^{77} +(-3150.15 + 7192.89i) q^{78} +12546.4 q^{79} -12633.8 q^{81} +(13405.4 - 30609.3i) q^{82} +6680.84 q^{83} +(-41673.2 + 38451.7i) q^{84} +(-37307.1 + 85185.1i) q^{86} -44088.2i q^{87} +(-18993.2 - 55015.1i) q^{88} +90400.9 q^{89} -20994.6i q^{91} +(28955.0 - 26716.7i) q^{92} +42820.2 q^{93} +(-120416. - 52736.8i) q^{94} +(55228.3 + 29682.5i) q^{96} +149616. i q^{97} +(22676.8 - 51779.1i) q^{98} +40460.4i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 - 36 * q^3 + 32 * q^4 + 204 * q^6 - 248 * q^8 + 1620 * q^9	$ 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9} - 1252 q^{12} - 2708 q^{14} + 3080 q^{16} - 2070 q^{18} - 8244 q^{22} - 1032 q^{24} - 8084 q^{26} - 11664 q^{27} - 22924 q^{28} + 7160 q^{31} - 14792 q^{32} - 21132 q^{34} + 18344 q^{36} + 3608 q^{37} + 16884 q^{38} + 44904 q^{39} + 11608 q^{41} + 49444 q^{42} + 51772 q^{43} - 72296 q^{44} - 28516 q^{46} + 85048 q^{48} - 18756 q^{49} + 111624 q^{52} - 928 q^{53} + 100584 q^{54} - 53624 q^{56} - 152344 q^{58} - 228648 q^{62} + 11264 q^{64} - 56688 q^{66} + 161604 q^{67} - 359040 q^{68} - 200312 q^{71} - 563448 q^{72} - 78876 q^{74} - 153872 q^{76} - 26008 q^{77} + 624640 q^{78} - 282080 q^{79} + 65172 q^{81} + 410576 q^{82} + 99092 q^{83} + 297128 q^{84} + 27452 q^{86} + 464496 q^{88} + 3160 q^{89} + 519244 q^{92} - 293472 q^{93} - 148820 q^{94} + 395168 q^{96} - 663674 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 36 * q^3 + 32 * q^4 + 204 * q^6 - 248 * q^8 + 1620 * q^9 - 1252 * q^12 - 2708 * q^14 + 3080 * q^16 - 2070 * q^18 - 8244 * q^22 - 1032 * q^24 - 8084 * q^26 - 11664 * q^27 - 22924 * q^28 + 7160 * q^31 - 14792 * q^32 - 21132 * q^34 + 18344 * q^36 + 3608 * q^37 + 16884 * q^38 + 44904 * q^39 + 11608 * q^41 + 49444 * q^42 + 51772 * q^43 - 72296 * q^44 - 28516 * q^46 + 85048 * q^48 - 18756 * q^49 + 111624 * q^52 - 928 * q^53 + 100584 * q^54 - 53624 * q^56 - 152344 * q^58 - 228648 * q^62 + 11264 * q^64 - 56688 * q^66 + 161604 * q^67 - 359040 * q^68 - 200312 * q^71 - 563448 * q^72 - 78876 * q^74 - 153872 * q^76 - 26008 * q^77 + 624640 * q^78 - 282080 * q^79 + 65172 * q^81 + 410576 * q^82 + 99092 * q^83 + 297128 * q^84 + 27452 * q^86 + 464496 * q^88 + 3160 * q^89 + 519244 * q^92 - 293472 * q^93 - 148820 * q^94 + 395168 * q^96 - 663674 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.26935	+	5.18171i	−0.401167	+	0.916005i
$2$	−2.26935	+	5.18171i	−0.401167	+	0.916005i
$3$	−10.8240			−0.694361			−0.347180	−	0.937798i	$-0.612861\pi$
$3$	−10.8240			−0.694361			−0.347180	+	0.937798i	$0.612861\pi$
$4$	−21.7001	−	23.5182i	−0.678130	−	0.734942i
$5$		0			0
$5$		0			0
$6$	24.5634	−	56.0868i	0.278555	−	0.636038i
$7$			163.706i			1.26276i	0.775475	+	0.631378i	$0.217510\pi$
$7$			163.706i			1.26276i	−0.775475	+	0.631378i	$0.782490\pi$
$8$	171.109	−	59.0729i	0.945254	−	0.326335i
$9$	−125.841			−0.517863
$10$		0			0
$11$		−	321.520i		−	0.801174i	−0.916259	−	0.400587i	$-0.868806\pi$
$11$		−	321.520i		−	0.801174i	0.916259	−	0.400587i	$-0.131194\pi$
$12$	234.883	+	254.561i	0.470867	+	0.510315i
$13$	−128.246			−0.210467			−0.105233	−	0.994448i	$-0.533559\pi$
$13$	−128.246			−0.210467			−0.105233	+	0.994448i	$0.533559\pi$
$14$	−848.277	−	371.506i	−1.15669	−	0.506577i
$15$		0			0
$16$	−82.2074	+	1020.69i	−0.0802807	+	0.996772i
$17$		−	2110.72i		−	1.77137i	−0.464290	−	0.885683i	$-0.653690\pi$
$17$		−	2110.72i		−	1.77137i	0.464290	−	0.885683i	$-0.346310\pi$
$18$	285.576	−	652.070i	0.207750	−	0.474365i
$19$		−	1454.37i		−	0.924252i	−0.886814	−	0.462126i	$-0.847087\pi$
$19$		−	1454.37i		−	0.924252i	0.886814	−	0.462126i	$-0.152913\pi$
$20$		0			0
$21$		−	1771.96i		−	0.876809i
$22$	1666.02	+	729.641i	0.733879	+	0.321405i
$23$			1231.18i			0.485289i	0.970115	+	0.242645i	$0.0780149\pi$
$23$			1231.18i			0.485289i	−0.970115	+	0.242645i	$0.921985\pi$
$24$	−1852.09	+	639.406i	−0.656347	+	0.226594i
$25$		0			0
$26$	291.033	−	664.531i	0.0844325	−	0.192789i
$27$	3992.34			1.05394
$28$	3850.07	−	3552.45i	0.928053	−	0.856313i
$29$			4073.19i			0.899372i	0.893187	+	0.449686i	$0.148464\pi$
$29$			4073.19i			0.899372i	−0.893187	+	0.449686i	$0.851536\pi$
$30$		0			0
$31$	−3956.03			−0.739360			−0.369680	−	0.929159i	$-0.620533\pi$
$31$	−3956.03			−0.739360			−0.369680	+	0.929159i	$0.620533\pi$
$32$	−5102.38	−	2742.28i	−0.880842	−	0.473410i
$33$			3480.14i			0.556304i
$34$	10937.1	+	4789.95i	1.62258	+	0.710615i
$35$		0			0
$36$	2730.76	+	2959.54i	0.351178	+	0.380600i
$37$	10656.6			1.27972			0.639861	−	0.768490i	$-0.278992\pi$
$37$	10656.6			1.27972			0.639861	+	0.768490i	$0.278992\pi$
$38$	7536.11	+	3300.46i	0.846620	+	0.370780i
$39$	1388.13			0.146140
$40$		0			0
$41$	−5907.19			−0.548809			−0.274404	−	0.961614i	$-0.588481\pi$
$41$	−5907.19			−0.548809			−0.274404	+	0.961614i	$0.588481\pi$
$42$	9181.76	+	4021.18i	0.803161	+	0.351747i
$43$	16439.6			1.35588			0.677938	−	0.735119i	$-0.262874\pi$
$43$	16439.6			1.35588			0.677938	+	0.735119i	$0.262874\pi$
$44$	−7561.57	+	6977.04i	−0.588817	+	0.543300i
$45$		0			0
$46$	−6379.59	−	2793.96i	−0.444527	−	0.194682i
$47$			23238.8i			1.53450i	0.641345	+	0.767252i	$0.278377\pi$
$47$			23238.8i			1.53450i	−0.641345	+	0.767252i	$0.721623\pi$
$48$	889.814	−	11048.0i	0.0557438	−	0.692120i
$49$	−9992.68			−0.594555
$50$		0			0
$51$			22846.5i			1.22997i
$52$	2782.95	+	3016.10i	0.142724	+	0.154681i
$53$	−30634.0			−1.49801			−0.749003	−	0.662567i	$-0.769467\pi$
$53$	−30634.0			−1.49801			−0.749003	+	0.662567i	$0.769467\pi$
$54$	−9059.99	+	20687.1i	−0.422808	+	0.965418i
$55$		0			0
$56$	9670.60	+	28011.6i	0.412082	+	1.19363i
$57$			15742.1i			0.641764i
$58$	−21106.1	−	9243.47i	−0.823829	−	0.360799i
$59$		−	25262.4i		−	0.944810i	−0.881382	−	0.472405i	$-0.843386\pi$
$59$		−	25262.4i		−	0.944810i	0.881382	−	0.472405i	$-0.156614\pi$
$60$		0			0
$61$			39115.5i			1.34594i	0.739672	+	0.672968i	$0.234981\pi$
$61$			39115.5i			1.34594i	−0.739672	+	0.672968i	$0.765019\pi$
$62$	8977.61	−	20499.0i	0.296607	−	0.677257i
$63$		−	20600.9i		−	0.653935i
$64$	25788.8	−	20215.9i	0.787011	−	0.616939i
$65$		0			0
$66$	−18033.1	−	7897.64i	−0.509577	−	0.223171i
$67$	20894.5			0.568651			0.284325	−	0.958728i	$-0.408230\pi$
$67$	20894.5			0.568651			0.284325	+	0.958728i	$0.408230\pi$
$68$	−49640.3	+	45803.0i	−1.30185	+	1.20122i
$69$		−	13326.3i		−	0.336966i
$70$		0			0
$71$	13889.1			0.326984			0.163492	−	0.986545i	$-0.447724\pi$
$71$	13889.1			0.326984			0.163492	+	0.986545i	$0.447724\pi$
$72$	−21532.5	+	7433.78i	−0.489512	+	0.168997i
$73$			43451.2i			0.954321i	0.878816	+	0.477161i	$0.158334\pi$
$73$			43451.2i			0.954321i	−0.878816	+	0.477161i	$0.841666\pi$
$74$	−24183.6	+	55219.6i	−0.513383	+	1.17223i
$75$		0			0
$76$	−34204.1	+	31560.0i	−0.679272	+	0.626763i
$77$	52634.8			1.01169
$78$	−3150.15	+	7192.89i	−0.0586266	+	0.133865i
$79$	12546.4			0.226179			0.113089	−	0.993585i	$-0.463925\pi$
$79$	12546.4			0.226179			0.113089	+	0.993585i	$0.463925\pi$
$80$		0			0
$81$	−12633.8			−0.213955
$82$	13405.4	−	30609.3i	0.220164	−	0.502711i
$83$	6680.84			0.106448			0.0532238	−	0.998583i	$-0.483050\pi$
$83$	6680.84			0.106448			0.0532238	+	0.998583i	$0.483050\pi$
$84$	−41673.2	+	38451.7i	−0.644404	+	0.594590i
$85$		0			0
$86$	−37307.1	+	85185.1i	−0.543933	+	1.24199i
$87$		−	44088.2i		−	0.624488i
$88$	−18993.2	−	55015.1i	−0.261451	−	0.757313i
$89$	90400.9			1.20976			0.604878	−	0.796318i	$-0.293222\pi$
$89$	90400.9			1.20976			0.604878	+	0.796318i	$0.293222\pi$
$90$		0			0
$91$		−	20994.6i		−	0.265769i
$92$	28955.0	−	26716.7i	0.356660	−	0.329089i
$93$	42820.2			0.513382
$94$	−120416.	−	52736.8i	−1.40561	−	0.615593i
$95$		0			0
$96$	55228.3	+	29682.5i	0.611622	+	0.328717i
$97$			149616.i			1.61454i	0.590184	+	0.807269i	$0.299055\pi$
$97$			149616.i			1.61454i	−0.590184	+	0.807269i	$0.700945\pi$
$98$	22676.8	−	51779.1i	0.238516	−	0.544615i
$99$			40460.4i			0.414898i
$100$		0			0
$101$			114822.i			1.12001i	0.828491	+	0.560003i	$0.189200\pi$
$101$			114822.i			1.12001i	−0.828491	+	0.560003i	$0.810800\pi$
$102$	−118384.	−	51846.5i	−1.12666	−	0.493423i
$103$		−	38586.9i		−	0.358382i	−0.983814	−	0.179191i	$-0.942652\pi$
$103$		−	38586.9i		−	0.358382i	0.983814	−	0.179191i	$-0.0573481\pi$
$104$	−21944.0	+	7575.84i	−0.198945	+	0.0686827i
$105$		0			0
$106$	69519.0	−	158736.i	0.600951	−	1.37218i
$107$	189459.			1.59976			0.799881	−	0.600158i	$-0.204896\pi$
$107$	189459.			1.59976			0.799881	+	0.600158i	$0.204896\pi$
$108$	−86634.3	−	93892.4i	−0.714711	−	0.774589i
$109$		−	24392.6i		−	0.196649i	−0.995154	−	0.0983245i	$-0.968652\pi$
$109$		−	24392.6i		−	0.196649i	0.995154	−	0.0983245i	$-0.0313483\pi$
$110$		0			0
$111$	−115348.			−0.888589
$112$	−167094.	−	13457.9i	−1.25868	−	0.101375i
$113$			52918.6i			0.389863i	0.980817	+	0.194932i	$0.0624485\pi$
$113$			52918.6i			0.389863i	−0.980817	+	0.194932i	$0.937552\pi$
$114$	−81571.0	−	35724.3i	−0.587859	−	0.257455i
$115$		0			0
$116$	95793.8	−	88388.7i	0.660987	−	0.609891i
$117$	16138.5			0.108993
$118$	130902.	+	57329.1i	0.865450	+	0.379027i
$119$	345538.			2.23681
$120$		0			0
$121$	57675.7			0.358120
$122$	−202685.	−	88766.6i	−1.23288	−	0.539945i
$123$	63939.5			0.381071
$124$	85846.5	+	93038.6i	0.501382	+	0.543387i
$125$		0			0
$126$	106748.	+	46750.5i	0.599008	+	0.262337i
$127$			293650.i			1.61555i	0.589489	+	0.807777i	$0.299329\pi$
$127$			293650.i			1.61555i	−0.589489	+	0.807777i	$0.700671\pi$
$128$	46229.0	+	179507.i	0.249396	+	0.968402i
$129$	−177942.			−0.941467
$130$		0			0
$131$		−	317738.i		−	1.61767i	−0.588032	−	0.808837i	$-0.700097\pi$
$131$		−	317738.i		−	1.61767i	0.588032	−	0.808837i	$-0.299903\pi$
$132$	81846.5	−	75519.6i	0.408851	−	0.377246i
$133$	238089.			1.16711
$134$	−47416.9	+	108269.i	−0.228124	+	0.520887i
$135$		0			0
$136$	−124687.	−	361164.i	−0.578059	−	1.67439i
$137$		−	162285.i		−	0.738717i	−0.929287	−	0.369358i	$-0.879577\pi$
$137$		−	162285.i		−	0.738717i	0.929287	−	0.369358i	$-0.120423\pi$
$138$	69052.8	+	30241.9i	0.308662	+	0.135180i
$139$		−	306759.i		−	1.34667i	−0.739338	−	0.673334i	$-0.764861\pi$
$139$		−	306759.i		−	1.34667i	0.739338	−	0.673334i	$-0.235139\pi$
$140$		0			0
$141$		−	251537.i		−	1.06550i
$142$	−31519.1	+	71969.0i	−0.131175	+	0.299519i
$143$			41233.5i			0.168621i
$144$	10345.0	−	128445.i	0.0415744	−	0.516192i
$145$		0			0
$146$	−225151.	−	98605.8i	−0.874163	−	0.382842i
$147$	108161.			0.412835
$148$	−231251.	−	250625.i	−0.867818	−	0.940523i
$149$		−	368107.i		−	1.35834i	−0.733981	−	0.679170i	$-0.762340\pi$
$149$		−	368107.i		−	1.35834i	0.733981	−	0.679170i	$-0.237660\pi$
$150$		0			0
$151$	336822.			1.20215			0.601075	−	0.799193i	$-0.294739\pi$
$151$	336822.			1.20215			0.601075	+	0.799193i	$0.294739\pi$
$152$	−85913.8	−	248856.i	−0.301616	−	0.873653i
$153$			265615.i			0.917326i
$154$	−119447.	+	272738.i	−0.405856	+	0.926711i
$155$		0			0
$156$	−30122.6	−	32646.3i	−0.0991018	−	0.107404i
$157$	−271253.			−0.878264			−0.439132	−	0.898423i	$-0.644714\pi$
$157$	−271253.			−0.878264			−0.439132	+	0.898423i	$0.644714\pi$
$158$	−28472.1	+	65011.8i	−0.0907356	+	0.207181i
$159$	331582.			1.04016
$160$		0			0
$161$	−201551.			−0.612802
$162$	28670.5	−	65464.6i	0.0858316	−	0.195983i
$163$	−121354.			−0.357756			−0.178878	−	0.983871i	$-0.557247\pi$
$163$	−121354.			−0.357756			−0.178878	+	0.983871i	$0.557247\pi$
$164$	128187.	+	138926.i	0.372163	+	0.403343i
$165$		0			0
$166$	−15161.1	+	34618.1i	−0.0427033	+	0.0975065i
$167$			56095.4i			0.155645i	0.996967	+	0.0778227i	$0.0247968\pi$
$167$			56095.4i			0.155645i	−0.996967	+	0.0778227i	$0.975203\pi$
$168$	−104675.	−	303198.i	−0.286133	−	0.828807i
$169$	−354846.			−0.955704
$170$		0			0
$171$			183019.i			0.478636i
$172$	−356741.	−	386629.i	−0.919459	−	0.996490i
$173$	167666.			0.425921			0.212960	−	0.977061i	$-0.431689\pi$
$173$	167666.			0.425921			0.212960	+	0.977061i	$0.431689\pi$
$174$	228452.	+	100051.i	0.572034	+	0.250524i
$175$		0			0
$176$	328174.	+	26431.4i	0.798588	+	0.0643188i
$177$			273440.i			0.656039i
$178$	−205151.	+	468431.i	−0.485314	+	1.10814i
$179$		−	535921.i		−	1.25017i	−0.780558	−	0.625083i	$-0.785065\pi$
$179$		−	535921.i		−	1.25017i	0.780558	−	0.625083i	$-0.214935\pi$
$180$		0			0
$181$		−	113446.i		−	0.257391i	−0.991684	−	0.128696i	$-0.958921\pi$
$181$		−	113446.i		−	0.257391i	0.991684	−	0.128696i	$-0.0410790\pi$
$182$	108788.	+	47643.9i	0.243445	+	0.106618i
$183$		−	423387.i		−	0.934565i
$184$	72729.2	+	210666.i	0.158367	+	0.458722i
$185$		0			0
$186$	−97173.7	+	221881.i	−0.205952	+	0.470261i
$187$	−678640.			−1.41917
$188$	546533.	−	504284.i	1.12777	−	1.04059i
$189$			653570.i			1.33088i
$190$		0			0
$191$	391808.			0.777124			0.388562	−	0.921423i	$-0.372972\pi$
$191$	391808.			0.777124			0.388562	+	0.921423i	$0.372972\pi$
$192$	−279138.	+	218817.i	−0.546470	+	0.428378i
$193$			261513.i			0.505359i	0.967550	+	0.252680i	$0.0813118\pi$
$193$			261513.i			0.505359i	−0.967550	+	0.252680i	$0.918688\pi$
$194$	−775265.	−	339530.i	−1.47892	−	0.647700i
$195$		0			0
$196$	216843.	+	235009.i	0.403185	+	0.436963i
$197$	898947.			1.65032			0.825161	−	0.564898i	$-0.191084\pi$
$197$	898947.			1.65032			0.825161	+	0.564898i	$0.191084\pi$
$198$	−209654.	−	91818.5i	−0.380049	−	0.166444i
$199$	83719.3			0.149862			0.0749312	−	0.997189i	$-0.476126\pi$
$199$	83719.3			0.149862			0.0749312	+	0.997189i	$0.476126\pi$
$200$		0			0
$201$	−226163.			−0.394849
$202$	−594972.	−	260570.i	−1.02593	−	0.449310i
$203$	−666805.			−1.13569
$204$	537307.	−	495772.i	0.903955	−	0.834077i
$205$		0			0
$206$	199946.	+	87566.9i	0.328280	+	0.143771i
$207$		−	154932.i		−	0.251313i
$208$	10542.7	−	130900.i	0.0168964	−	0.209788i
$209$	−467609.			−0.740487
$210$		0			0
$211$			553641.i			0.856095i	0.903756	+	0.428047i	$0.140798\pi$
$211$			553641.i			0.856095i	−0.903756	+	0.428047i	$0.859202\pi$
$212$	664761.	+	720454.i	1.01584	+	1.10095i
$213$	−150335.			−0.227045
$214$	−429948.	+	981720.i	−0.641772	+	1.46539i
$215$		0			0
$216$	683126.	−	235839.i	0.996246	−	0.343939i
$217$		−	647627.i		−	0.933632i
$218$	126395.	+	55355.2i	0.180131	+	0.0788892i
$219$		−	470316.i		−	0.662643i
$220$		0			0
$221$			270691.i			0.372814i
$222$	261764.	−	597697.i	0.356473	−	0.813952i
$223$		−	279400.i		−	0.376239i	−0.982146	−	0.188120i	$-0.939761\pi$
$223$		−	279400.i		−	0.376239i	0.982146	−	0.188120i	$-0.0602392\pi$
$224$	448929.	−	835291.i	0.597802	−	1.11229i
$225$		0			0
$226$	−274209.	−	120091.i	−0.357116	−	0.156400i
$227$	593068.			0.763905			0.381953	−	0.924182i	$-0.375252\pi$
$227$	593068.			0.763905			0.381953	+	0.924182i	$0.375252\pi$
$228$	370225.	−	341606.i	0.471660	−	0.435199i
$229$			927873.i			1.16923i	0.811311	+	0.584615i	$0.198754\pi$
$229$			927873.i			1.16923i	−0.811311	+	0.584615i	$0.801246\pi$
$230$		0			0
$231$	−569720.			−0.702476
$232$	240615.	+	696960.i	0.293496	+	0.850135i
$233$			1.09279e6i			1.31871i	0.751833	+	0.659353i	$0.229170\pi$
$233$			1.09279e6i			1.31871i	−0.751833	+	0.659353i	$0.770830\pi$
$234$	−36623.9	+	83625.0i	−0.0437245	+	0.0998382i
$235$		0			0
$236$	−594125.	+	548197.i	−0.694381	+	0.640703i
$237$	−135803.			−0.157050
$238$	−784145.	+	1.79048e6i	−0.897333	+	2.04892i
$239$	797967.			0.903630			0.451815	−	0.892112i	$-0.350777\pi$
$239$	797967.			0.903630			0.451815	+	0.892112i	$0.350777\pi$
$240$		0			0
$241$	−1.61861e6			−1.79515			−0.897573	−	0.440865i	$-0.854672\pi$
$241$	−1.61861e6			−1.79515			−0.897573	+	0.440865i	$0.854672\pi$
$242$	−130886.	+	298858.i	−0.143666	+	0.328040i
$243$	−833389.			−0.905383
$244$	919924.	−	848812.i	0.989185	−	0.912719i
$245$		0			0
$246$	−145101.	+	331315.i	−0.152873	+	0.349063i
$247$			186516.i			0.194525i
$248$	−676914.	+	233695.i	−0.698883	+	0.241279i
$249$	−72313.5			−0.0739130
$250$		0			0
$251$			449688.i			0.450533i	0.974297	+	0.225266i	$0.0723253\pi$
$251$			449688.i			0.450533i	−0.974297	+	0.225266i	$0.927675\pi$
$252$	−484495.	+	447042.i	−0.480605	+	0.443453i
$253$	395848.			0.388801
$254$	−1.52161e6	−	666394.i	−1.47985	−	0.648107i
$255$		0			0
$256$	−1.03506e6	−	167817.i	−0.987110	−	0.160043i
$257$			396434.i			0.374402i	0.982322	+	0.187201i	$0.0599416\pi$
$257$			396434.i			0.374402i	−0.982322	+	0.187201i	$0.940058\pi$
$258$	403813.	−	922045.i	0.377686	−	0.862388i
$259$			1.74456e6i			1.61598i
$260$		0			0
$261$		−	512573.i		−	0.465752i
$262$	1.64643e6	+	721058.i	1.48180	+	0.648958i
$263$		−	1.93423e6i		−	1.72432i	−0.506635	−	0.862160i	$-0.669111\pi$
$263$		−	1.93423e6i		−	1.72432i	0.506635	−	0.862160i	$-0.330889\pi$
$264$	205582.	+	595484.i	0.181541	+	0.525848i
$265$		0			0
$266$	−540306.	+	1.23371e6i	−0.468205	+	1.06907i
$267$	−978500.			−0.840007
$268$	−453414.	−	491401.i	−0.385619	−	0.417926i
$269$			670016.i			0.564553i	0.959333	+	0.282276i	$0.0910895\pi$
$269$			670016.i			0.564553i	−0.959333	+	0.282276i	$0.908910\pi$
$270$		0			0
$271$	2.08940e6			1.72822			0.864109	−	0.503305i	$-0.167883\pi$
$271$	2.08940e6			1.72822			0.864109	+	0.503305i	$0.167883\pi$
$272$	2.15440e6	+	173517.i	1.76565	+	0.142207i
$273$			227246.i			0.184539i
$274$	840915.	+	368281.i	0.676668	+	0.296349i
$275$		0			0
$276$	−313409.	+	289182.i	−0.247651	+	0.228506i
$277$	−828834.			−0.649035			−0.324517	−	0.945880i	$-0.605202\pi$
$277$	−828834.			−0.649035			−0.324517	+	0.945880i	$0.605202\pi$
$278$	1.58954e6	+	696143.i	1.23356	+	0.540240i
$279$	497830.			0.382887
$280$		0			0
$281$	2.39932e6			1.81268			0.906342	−	0.422545i	$-0.138863\pi$
$281$	2.39932e6			1.81268			0.906342	+	0.422545i	$0.138863\pi$
$282$	1.30339e6	+	570823.i	0.976003	+	0.427444i
$283$	2.00868e6			1.49089			0.745444	−	0.666568i	$-0.232237\pi$
$283$	2.00868e6			1.49089			0.745444	+	0.666568i	$0.232237\pi$
$284$	−301395.	−	326645.i	−0.221738	−	0.240315i
$285$		0			0
$286$	−213660.	−	93573.2i	−0.154457	−	0.0676451i
$287$		−	967042.i		−	0.693012i
$288$	642088.	+	345091.i	0.456156	+	0.245162i
$289$	−3.03529e6			−2.13774
$290$		0			0
$291$		−	1.61944e6i		−	1.12107i
$292$	1.02189e6	−	942897.i	0.701371	−	0.647153i
$293$	1.74203e6			1.18546			0.592729	−	0.805402i	$-0.298050\pi$
$293$	1.74203e6			1.18546			0.592729	+	0.805402i	$0.298050\pi$
$294$	−245454.	+	560458.i	−0.165616	+	0.378159i
$295$		0			0
$296$	1.82345e6	−	629519.i	1.20966	−	0.417618i
$297$		−	1.28362e6i		−	0.844393i
$298$	1.90742e6	+	835362.i	1.24425	+	0.544922i
$299$		−	157893.i		−	0.102137i
$300$		0			0
$301$			2.69126e6i			1.71214i
$302$	−764366.	+	1.74531e6i	−0.482263	+	1.10118i
$303$		−	1.24283e6i		−	0.777688i
$304$	1.48447e6	+	119560.i	0.921269	+	0.0741996i
$305$		0			0
$306$	−1.37634e6	−	602772.i	−0.840275	−	0.368001i
$307$	978690.			0.592651			0.296326	−	0.955087i	$-0.404239\pi$
$307$	978690.			0.592651			0.296326	+	0.955087i	$0.404239\pi$
$308$	−1.14218e6	−	1.23787e6i	−0.686055	−	0.743532i
$309$			417665.i			0.248847i
$310$		0			0
$311$	−1.57652e6			−0.924268			−0.462134	−	0.886810i	$-0.652916\pi$
$311$	−1.57652e6			−0.924268			−0.462134	+	0.886810i	$0.652916\pi$
$312$	237522.	−	82001.0i	0.138139	−	0.0476906i
$313$		−	1.60962e6i		−	0.928670i	−0.885660	−	0.464335i	$-0.846293\pi$
$313$		−	1.60962e6i		−	0.928670i	0.885660	−	0.464335i	$-0.153707\pi$
$314$	615566.	−	1.40555e6i	0.352331	−	0.804494i
$315$		0			0
$316$	−272259.	−	295069.i	−0.153379	−	0.166228i
$317$	−1.50670e6			−0.842130			−0.421065	−	0.907030i	$-0.638344\pi$
$317$	−1.50670e6			−0.842130			−0.421065	+	0.907030i	$0.638344\pi$
$318$	−752475.	+	1.71816e6i	−0.417277	+	0.952788i
$319$	1.30961e6			0.720553
$320$		0			0
$321$	−2.05070e6			−1.11081
$322$	457389.	−	1.04438e6i	0.245836	−	0.561330i
$323$	−3.06977e6			−1.63719
$324$	274155.	+	297124.i	0.145089	+	0.157244i
$325$		0			0
$326$	275395.	−	628823.i	0.143520	−	0.327706i
$327$			264026.i			0.136545i
$328$	−1.01077e6	+	348955.i	−0.518764	+	0.179095i
$329$	−3.80433e6			−1.93771
$330$		0			0
$331$			394453.i			0.197891i	0.995093	+	0.0989454i	$0.0315469\pi$
$331$			394453.i			0.197891i	−0.995093	+	0.0989454i	$0.968453\pi$
$332$	−144975.	−	157121.i	−0.0721852	−	0.0782328i
$333$	−1.34104e6			−0.662721
$334$	−290670.	−	127300.i	−0.142572	−	0.0624398i
$335$		0			0
$336$	1.80863e6	+	145668.i	0.873979	+	0.0703908i
$337$		−	1.36879e6i		−	0.656543i	−0.944583	−	0.328272i	$-0.893534\pi$
$337$		−	1.36879e6i		−	0.656543i	0.944583	−	0.328272i	$-0.106466\pi$
$338$	805268.	−	1.83871e6i	0.383397	−	0.875429i
$339$		−	572791.i		−	0.270706i
$340$		0			0
$341$			1.27195e6i			0.592356i
$342$	−948350.	−	415333.i	−0.438433	−	0.192013i
$343$			1.11555e6i			0.511979i
$344$	2.81297e6	−	971135.i	1.28165	−	0.442470i
$345$		0			0
$346$	−380491.	+	868794.i	−0.170865	+	0.390145i
$347$	569376.			0.253849			0.126925	−	0.991912i	$-0.459489\pi$
$347$	569376.			0.253849			0.126925	+	0.991912i	$0.459489\pi$
$348$	−1.03687e6	+	956721.i	−0.458963	+	0.423484i
$349$			2.20053e6i			0.967081i	0.875322	+	0.483541i	$0.160649\pi$
$349$			2.20053e6i			0.967081i	−0.875322	+	0.483541i	$0.839351\pi$
$350$		0			0
$351$	−511999.			−0.221820
$352$	−881700.	+	1.64052e6i	−0.379284	+	0.705708i
$353$			2.51557e6i			1.07448i	0.843428	+	0.537242i	$0.180534\pi$
$353$			2.51557e6i			1.07448i	−0.843428	+	0.537242i	$0.819466\pi$
$354$	−1.41689e6	−	620531.i	−0.600935	−	0.263181i
$355$		0			0
$356$	−1.96171e6	−	2.12606e6i	−0.820371	−	0.889100i
$357$	−3.74011e6			−1.55315
$358$	2.77698e6	+	1.21619e6i	1.14516	+	0.501526i
$359$	794808.			0.325481			0.162741	−	0.986669i	$-0.447967\pi$
$359$	794808.			0.325481			0.162741	+	0.986669i	$0.447967\pi$
$360$		0			0
$361$	360911.			0.145758
$362$	587845.	+	257449.i	0.235772	+	0.103257i
$363$	−624282.			−0.248665
$364$	−493754.	+	455585.i	−0.195325	+	0.180225i
$365$		0			0
$366$	2.19386e6	+	960810.i	0.856066	+	0.374917i
$367$		−	874302.i		−	0.338841i	−0.985544	−	0.169421i	$-0.945810\pi$
$367$		−	874302.i		−	0.338841i	0.985544	−	0.169421i	$-0.0541896\pi$
$368$	−1.25666e6	−	101212.i	−0.483723	−	0.0389594i
$369$	743365.			0.284208
$370$		0			0
$371$		−	5.01497e6i		−	1.89162i
$372$	−929204.	−	1.00705e6i	−0.348140	−	0.377306i
$373$	−4.86205e6			−1.80945			−0.904726	−	0.425994i	$-0.859924\pi$
$373$	−4.86205e6			−1.80945			−0.904726	+	0.425994i	$0.859924\pi$
$374$	1.54007e6	−	3.51651e6i	0.569326	−	1.29997i
$375$		0			0
$376$	1.37278e6	+	3.97637e6i	0.500763	+	1.45050i
$377$		−	522368.i		−	0.189288i
$378$	−3.38661e6	−	1.48318e6i	−1.21909	−	0.533904i
$379$		−	1.24150e6i		−	0.443964i	−0.975051	−	0.221982i	$-0.928747\pi$
$379$		−	1.24150e6i		−	0.443964i	0.975051	−	0.221982i	$-0.0712527\pi$
$380$		0			0
$381$		−	3.17848e6i		−	1.12178i
$382$	−889149.	+	2.03024e6i	−0.311757	+	0.711849i
$383$			30969.9i			0.0107880i	0.999985	+	0.00539402i	$0.00171698\pi$
$383$			30969.9i			0.0107880i	−0.999985	+	0.00539402i	$0.998283\pi$
$384$	−500383.	−	1.94298e6i	−0.173171	−	0.672420i
$385$		0			0
$386$	−1.35508e6	−	593463.i	−0.462911	−	0.202734i
$387$	−2.06877e6			−0.702158
$388$	3.51869e6	−	3.24669e6i	1.18659	−	1.09487i
$389$		−	4.27860e6i		−	1.43360i	−0.697279	−	0.716800i	$-0.745606\pi$
$389$		−	4.27860e6i		−	1.43360i	0.697279	−	0.716800i	$-0.254394\pi$
$390$		0			0
$391$	2.59867e6			0.859626
$392$	−1.70984e6	+	590297.i	−0.562005	+	0.194024i
$393$			3.43920e6i			1.12325i
$394$	−2.04002e6	+	4.65808e6i	−0.662055	+	1.51170i
$395$		0			0
$396$	951553.	−	877996.i	0.304926	−	0.281355i
$397$	2.31119e6			0.735968			0.367984	−	0.929832i	$-0.380048\pi$
$397$	2.31119e6			0.735968			0.367984	+	0.929832i	$0.380048\pi$
$398$	−189988.	+	433809.i	−0.0601199	+	0.137275i
$399$	−2.57708e6			−0.810392
$400$		0			0
$401$	996347.			0.309421			0.154710	−	0.987960i	$-0.450556\pi$
$401$	996347.			0.309421			0.154710	+	0.987960i	$0.450556\pi$
$402$	513241.	−	1.17191e6i	0.158400	−	0.361683i
$403$	507344.			0.155611
$404$	2.70039e6	−	2.49165e6i	0.823140	−	0.759509i
$405$		0			0
$406$	1.51321e6	−	3.45519e6i	0.455601	−	1.04030i
$407$		−	3.42633e6i		−	1.02528i
$408$	1.34961e6	+	3.90924e6i	0.401381	+	1.16263i
$409$	5.17948e6			1.53101			0.765505	−	0.643430i	$-0.222489\pi$
$409$	5.17948e6			1.53101			0.765505	+	0.643430i	$0.222489\pi$
$410$		0			0
$411$			1.75658e6i			0.512936i
$412$	−907492.	+	837341.i	−0.263390	+	0.243030i
$413$	4.13561e6			1.19306
$414$	802813.	+	351595.i	0.230204	+	0.100819i
$415$		0			0
$416$	654358.	+	351686.i	0.185388	+	0.0996371i
$417$			3.32037e6i			0.935074i
$418$	1.06117e6	−	2.42301e6i	0.297059	−	0.678289i
$419$			3.57698e6i			0.995363i	0.867360	+	0.497682i	$0.165815\pi$
$419$			3.57698e6i			0.995363i	−0.867360	+	0.497682i	$0.834185\pi$
$420$		0			0
$421$		−	2.15848e6i		−	0.593531i	−0.954950	−	0.296765i	$-0.904092\pi$
$421$		−	2.15848e6i		−	0.593531i	0.954950	−	0.296765i	$-0.0959080\pi$
$422$	−2.86880e6	−	1.25640e6i	−0.784187	−	0.343437i
$423$		−	2.92438e6i		−	0.794664i
$424$	−5.24175e6	+	1.80964e6i	−1.41600	+	0.488852i
$425$		0			0
$426$	341163.	−	778993.i	0.0910831	−	0.207974i
$427$	−6.40344e6			−1.69959
$428$	−4.11128e6	−	4.45572e6i	−1.08485	−	1.17573i
$429$		−	446312.i		−	0.117084i
$430$		0			0
$431$	−1.80890e6			−0.469052			−0.234526	−	0.972110i	$-0.575354\pi$
$431$	−1.80890e6			−0.469052			−0.234526	+	0.972110i	$0.575354\pi$
$432$	−328200.	+	4.07496e6i	−0.0846114	+	1.05054i
$433$		−	1.28911e6i		−	0.330423i	−0.986258	−	0.165211i	$-0.947169\pi$
$433$		−	1.28911e6i		−	0.330423i	0.986258	−	0.165211i	$-0.0528306\pi$
$434$	3.35581e6	+	1.46969e6i	0.855211	+	0.374542i
$435$		0			0
$436$	−573669.	+	529323.i	−0.144526	+	0.133354i
$437$	1.79058e6			0.448530
$438$	2.43704e6	+	1.06731e6i	0.606984	+	0.265831i
$439$	−1.89694e6			−0.469777			−0.234889	−	0.972022i	$-0.575473\pi$
$439$	−1.89694e6			−0.469777			−0.234889	+	0.972022i	$0.575473\pi$
$440$		0			0
$441$	1.25749e6			0.307898
$442$	−1.40264e6	−	614290.i	−0.341500	−	0.149561i
$443$	6.01979e6			1.45738			0.728689	−	0.684845i	$-0.240130\pi$
$443$	6.01979e6			1.45738			0.728689	+	0.684845i	$0.240130\pi$
$444$	2.50306e6	+	2.71276e6i	0.602579	+	0.653062i
$445$		0			0
$446$	1.44777e6	+	634055.i	0.344637	+	0.150935i
$447$			3.98440e6i			0.943178i
$448$	3.30946e6	+	4.22178e6i	0.779044	+	0.993803i
$449$	2.40081e6			0.562007			0.281003	−	0.959707i	$-0.409333\pi$
$449$	2.40081e6			0.562007			0.281003	+	0.959707i	$0.409333\pi$
$450$		0			0
$451$			1.89928e6i			0.439691i
$452$	1.24455e6	−	1.14834e6i	0.286527	−	0.264378i
$453$	−3.64577e6			−0.834726
$454$	−1.34588e6	+	3.07310e6i	−0.306454	+	0.699741i
$455$		0			0
$456$	929933.	+	2.69362e6i	0.209430	+	0.606631i
$457$		−	858952.i		−	0.192388i	−0.995363	−	0.0961941i	$-0.969333\pi$
$457$		−	858952.i		−	0.192388i	0.995363	−	0.0961941i	$-0.0306669\pi$
$458$	−4.80797e6	−	2.10567e6i	−1.07102	−	0.469057i
$459$		−	8.42671e6i		−	1.86692i
$460$		0			0
$461$		−	2.33481e6i		−	0.511680i	−0.966719	−	0.255840i	$-0.917648\pi$
$461$		−	2.33481e6i		−	0.511680i	0.966719	−	0.255840i	$-0.0823521\pi$
$462$	1.29289e6	−	2.95212e6i	0.281811	−	0.643472i
$463$			1.35195e6i			0.293096i	0.989204	+	0.146548i	$0.0468162\pi$
$463$			1.35195e6i			0.293096i	−0.989204	+	0.146548i	$0.953184\pi$
$464$	−4.15748e6	−	334846.i	−0.896469	−	0.0722022i
$465$		0			0
$466$	−5.66253e6	−	2.47993e6i	−1.20794	−	0.529022i
$467$	6.44013e6			1.36648			0.683239	−	0.730195i	$-0.260571\pi$
$467$	6.44013e6			1.36648			0.683239	+	0.730195i	$0.260571\pi$
$468$	−350208.	−	379548.i	−0.0739114	−	0.0801036i
$469$			3.42056e6i			0.718068i
$470$		0			0
$471$	2.93604e6			0.609832
$472$	−1.49232e6	−	4.32263e6i	−0.308324	−	0.893085i
$473$		−	5.28566e6i		−	1.08629i
$474$	308183.	−	703689.i	0.0630032	−	0.143858i
$475$		0			0
$476$	−7.49822e6	−	8.12641e6i	−1.51684	−	1.64392i
$477$	3.85500e6			0.775762
$478$	−1.81086e6	+	4.13483e6i	−0.362507	+	0.827729i
$479$	1.85358e6			0.369124			0.184562	−	0.982821i	$-0.440913\pi$
$479$	1.85358e6			0.369124			0.184562	+	0.982821i	$0.440913\pi$
$480$		0			0
$481$	−1.36667e6			−0.269339
$482$	3.67319e6	−	8.38717e6i	0.720154	−	1.64436i
$483$	2.18159e6			0.425506
$484$	−1.25157e6	−	1.35643e6i	−0.242852	−	0.263198i
$485$		0			0
$486$	1.89125e6	−	4.31838e6i	0.363210	−	0.829335i
$487$			2.51668e6i			0.480846i	0.970668	+	0.240423i	$0.0772861\pi$
$487$			2.51668e6i			0.480846i	−0.970668	+	0.240423i	$0.922714\pi$
$488$	2.31067e6	+	6.69302e6i	0.439226	+	1.27225i
$489$	1.31354e6			0.248412
$490$		0			0
$491$			5.39115e6i			1.00920i	0.863353	+	0.504601i	$0.168360\pi$
$491$			5.39115e6i			1.00920i	−0.863353	+	0.504601i	$0.831640\pi$
$492$	−1.38750e6	−	1.50374e6i	−0.258416	−	0.280065i
$493$	8.59736e6			1.59312
$494$	−966472.	−	423270.i	−0.178185	−	0.0780369i
$495$		0			0
$496$	325215.	−	4.03790e6i	0.0593563	−	0.736973i
$497$			2.27372e6i			0.412902i
$498$	164104.	−	374707.i	0.0296515	−	0.0677047i
$499$			3.18358e6i			0.572353i	0.958177	+	0.286177i	$0.0923844\pi$
$499$			3.18358e6i			0.572353i	−0.958177	+	0.286177i	$0.907616\pi$
$500$		0			0
$501$		−	607177.i		−	0.108074i
$502$	−2.33015e6	−	1.02050e6i	−0.412690	−	0.180739i
$503$			8.99291e6i			1.58482i	0.609989	+	0.792410i	$0.291174\pi$
$503$			8.99291e6i			1.58482i	−0.609989	+	0.792410i	$0.708826\pi$
$504$	−1.21696e6	−	3.52500e6i	−0.213402	−	0.618135i
$505$		0			0
$506$	−898317.	+	2.05117e6i	−0.155974	+	0.356144i
$507$	3.84086e6			0.663603
$508$	6.90612e6	−	6.37226e6i	1.18734	−	1.09555i
$509$		−	5.35388e6i		−	0.915956i	−0.888964	−	0.457978i	$-0.848574\pi$
$509$		−	5.35388e6i		−	0.915956i	0.888964	−	0.457978i	$-0.151426\pi$
$510$		0			0
$511$	−7.11322e6			−1.20508
$512$	3.21849e6	−	4.98254e6i	0.542597	−	0.839993i
$513$		−	5.80633e6i		−	0.974111i
$514$	−2.05420e6	−	899646.i	−0.342954	−	0.150198i
$515$		0			0
$516$	3.86137e6	+	4.18488e6i	0.638436	+	0.691924i
$517$	7.47173e6			1.22941
$518$	−9.03978e6	−	3.95900e6i	−1.48024	−	0.648278i
$519$	−1.81481e6			−0.295743
$520$		0			0
$521$	−2.62401e6			−0.423518			−0.211759	−	0.977322i	$-0.567919\pi$
$521$	−2.62401e6			−0.423518			−0.211759	+	0.977322i	$0.567919\pi$
$522$	2.65600e6	+	1.16320e6i	0.426631	+	0.186844i
$523$	1.31228e6			0.209784			0.104892	−	0.994484i	$-0.466550\pi$
$523$	1.31228e6			0.209784			0.104892	+	0.994484i	$0.466550\pi$
$524$	−7.47262e6	+	6.89497e6i	−1.18890	+	1.09699i
$525$		0			0
$526$	1.00226e7	+	4.38943e6i	1.57949	+	0.691741i
$527$			8.35008e6i			1.30968i
$528$	−3.55216e6	−	286093.i	−0.554508	−	0.0446605i
$529$	4.92055e6			0.764494
$530$		0			0
$531$			3.17904e6i			0.489282i
$532$	−5.16657e6	−	5.59941e6i	−0.791449	−	0.857756i
$533$	757570.			0.115506
$534$	2.22055e6	−	5.07030e6i	0.336983	−	0.769450i
$535$		0			0
$536$	3.57525e6	−	1.23430e6i	0.537520	−	0.185571i
$537$			5.80081e6i			0.868067i
$538$	−3.47183e6	−	1.52050e6i	−0.517133	−	0.226480i
$539$			3.21285e6i			0.476342i
$540$		0			0
$541$			6.84935e6i			1.00613i	0.864247	+	0.503067i	$0.167795\pi$
$541$			6.84935e6i			1.00613i	−0.864247	+	0.503067i	$0.832205\pi$
$542$	−4.74157e6	+	1.08267e7i	−0.693304	+	1.58306i
$543$			1.22794e6i			0.178722i
$544$	−5.78820e6	+	1.07697e7i	−0.838583	+	1.56029i
$545$		0			0
$546$	−1.17752e6	−	515698.i	−0.169039	−	0.0740311i
$547$	6.39084e6			0.913251			0.456625	−	0.889659i	$-0.349058\pi$
$547$	6.39084e6			0.913251			0.456625	+	0.889659i	$0.349058\pi$
$548$	−3.81665e6	+	3.52162e6i	−0.542914	+	0.500946i
$549$		−	4.92232e6i		−	0.697010i
$550$		0			0
$551$	5.92391e6			0.831246
$552$	−787222.	−	2.28025e6i	−0.109964	−	0.318518i
$553$			2.05392e6i			0.285609i
$554$	1.88091e6	−	4.29477e6i	0.260372	−	0.594519i
$555$		0			0
$556$	−7.21441e6	+	6.65672e6i	−0.989724	+	0.913216i
$557$	−463389.			−0.0632861			−0.0316430	−	0.999499i	$-0.510074\pi$
$557$	−463389.			−0.0632861			−0.0316430	+	0.999499i	$0.510074\pi$
$558$	−1.12975e6	+	2.57961e6i	−0.153602	+	0.350726i
$559$	−2.10830e6			−0.285367
$560$		0			0
$561$	7.34561e6			0.985418
$562$	−5.44488e6	+	1.24326e7i	−0.727189	+	1.66043i
$563$	−1.07609e7			−1.43080			−0.715400	−	0.698715i	$-0.753756\pi$
$563$	−1.07609e7			−1.43080			−0.715400	+	0.698715i	$0.753756\pi$
$564$	−5.91568e6	+	5.45838e6i	−0.783081	+	0.722547i
$565$		0			0
$566$	−4.55839e6	+	1.04084e7i	−0.598096	+	1.36566i
$567$		−	2.06823e6i		−	0.270173i
$568$	2.37655e6	−	820467.i	0.309083	−	0.106706i
$569$	1.04253e7			1.34992			0.674961	−	0.737853i	$-0.264160\pi$
$569$	1.04253e7			1.34992			0.674961	+	0.737853i	$0.264160\pi$
$570$		0			0
$571$			1.58675e6i			0.203666i	0.994802	+	0.101833i	$0.0324707\pi$
$571$			1.58675e6i			0.203666i	−0.994802	+	0.101833i	$0.967529\pi$
$572$	969737.	−	894774.i	0.123926	−	0.114347i
$573$	−4.24094e6			−0.539605
$574$	5.01093e6	+	2.19455e6i	0.634802	+	0.278014i
$575$		0			0
$576$	−3.24528e6	+	2.54398e6i	−0.407564	+	0.319490i
$577$		−	2.79056e6i		−	0.348941i	−0.984662	−	0.174471i	$-0.944179\pi$
$577$		−	2.79056e6i		−	0.348941i	0.984662	−	0.174471i	$-0.0558214\pi$
$578$	6.88811e6	−	1.57280e7i	0.857592	−	1.95818i
$579$		−	2.83062e6i		−	0.350901i
$580$		0			0
$581$			1.09369e6i			0.134417i
$582$	8.39148e6	+	3.67508e6i	1.02691	+	0.449737i
$583$			9.84944e6i			1.20016i
$584$	2.56679e6	+	7.43490e6i	0.311428	+	0.902076i
$585$		0			0
$586$	−3.95327e6	+	9.02668e6i	−0.475567	+	1.08589i
$587$	1.94272e6			0.232710			0.116355	−	0.993208i	$-0.462879\pi$
$587$	1.94272e6			0.232710			0.116355	+	0.993208i	$0.462879\pi$
$588$	−2.34711e6	−	2.54374e6i	−0.279956	−	0.303410i
$589$			5.75353e6i			0.683355i
$590$		0			0
$591$	−9.73022e6			−1.14592
$592$	−876055.	+	1.08772e7i	−0.102737	+	1.27559i
$593$		−	8.14862e6i		−	0.951584i	−0.879558	−	0.475792i	$-0.842161\pi$
$593$		−	8.14862e6i		−	0.951584i	0.879558	−	0.475792i	$-0.157839\pi$
$594$	6.65133e6	+	2.91297e6i	0.773468	+	0.338743i
$595$		0			0
$596$	−8.65720e6	+	7.98798e6i	−0.998302	+	0.921131i
$597$	−906179.			−0.104059
$598$	818154.	+	358313.i	0.0935583	+	0.0409742i
$599$	−1.49677e6			−0.170447			−0.0852234	−	0.996362i	$-0.527160\pi$
$599$	−1.49677e6			−0.170447			−0.0852234	+	0.996362i	$0.527160\pi$
$600$		0			0
$601$	−9.04082e6			−1.02099			−0.510495	−	0.859881i	$-0.670538\pi$
$601$	−9.04082e6			−1.02099			−0.510495	+	0.859881i	$0.670538\pi$
$602$	−1.39453e7	−	6.10740e6i	−1.56833	−	0.686855i
$603$	−2.62938e6			−0.294483
$604$	−7.30910e6	−	7.92144e6i	−0.815213	−	0.883511i
$605$		0			0
$606$	6.43998e6	+	2.82041e6i	0.712366	+	0.311983i
$607$		−	3.63200e6i		−	0.400105i	−0.979785	−	0.200052i	$-0.935889\pi$
$607$		−	3.63200e6i		−	0.400105i	0.979785	−	0.200052i	$-0.0641112\pi$
$608$	−3.98829e6	+	7.42075e6i	−0.437550	+	0.814120i
$609$	7.21751e6			0.788577
$610$		0			0
$611$		−	2.98027e6i		−	0.322962i
$612$	6.24677e6	−	5.76388e6i	0.674182	−	0.622066i
$613$	−1.89937e6			−0.204154			−0.102077	−	0.994776i	$-0.532549\pi$
$613$	−1.89937e6			−0.204154			−0.102077	+	0.994776i	$0.532549\pi$
$614$	−2.22099e6	+	5.07128e6i	−0.237752	+	0.542871i
$615$		0			0
$616$	9.00631e6	−	3.10929e6i	0.956302	−	0.330149i
$617$			5.96746e6i			0.631069i	0.948914	+	0.315534i	$0.102184\pi$
$617$			5.96746e6i			0.631069i	−0.948914	+	0.315534i	$0.897816\pi$
$618$	−2.16422e6	−	947826.i	−0.227945	−	0.0998291i
$619$			1.46307e7i			1.53475i	0.641196	+	0.767377i	$0.278439\pi$
$619$			1.46307e7i			1.53475i	−0.641196	+	0.767377i	$0.721561\pi$
$620$		0			0
$621$			4.91527e6i			0.511468i
$622$	3.57766e6	−	8.16905e6i	0.370786	−	0.846634i
$623$			1.47992e7i			1.52763i
$624$	−114115.	+	1.41686e6i	−0.0117322	+	0.145668i
$625$		0			0
$626$	8.34055e6	+	3.65277e6i	0.850666	+	0.372552i
$627$	5.06141e6			0.514165
$628$	5.88622e6	+	6.37936e6i	0.595577	+	0.645473i
$629$		−	2.24932e7i		−	2.26686i
$630$		0			0
$631$	−1.47747e7			−1.47722			−0.738609	−	0.674134i	$-0.764517\pi$
$631$	−1.47747e7			−1.47722			−0.738609	+	0.674134i	$0.764517\pi$
$632$	2.14681e6	−	741154.i	0.213796	−	0.0738101i
$633$		−	5.99261e6i		−	0.594438i
$634$	3.41923e6	−	7.80729e6i	0.337835	−	0.771395i
$635$		0			0
$636$	−7.19538e6	−	7.79821e6i	−0.705361	−	0.764455i
$637$	1.28152e6			0.125134
$638$	−2.97196e6	+	6.78603e6i	−0.289062	+	0.660030i
$639$	−1.74781e6			−0.169333
$640$		0			0
$641$	1.81017e7			1.74010			0.870050	−	0.492964i	$-0.164087\pi$
$641$	1.81017e7			1.74010			0.870050	+	0.492964i	$0.164087\pi$
$642$	4.65376e6	−	1.06261e7i	0.445622	−	1.01751i
$643$	7.21849e6			0.688524			0.344262	−	0.938874i	$-0.388129\pi$
$643$	7.21849e6			0.688524			0.344262	+	0.938874i	$0.388129\pi$
$644$	4.37369e6	+	4.74011e6i	0.415559	+	0.450374i
$645$		0			0
$646$	6.96636e6	−	1.59066e7i	0.656787	−	1.49967i
$647$			2.44672e6i			0.229786i	0.993378	+	0.114893i	$0.0366526\pi$
$647$			2.44672e6i			0.229786i	−0.993378	+	0.114893i	$0.963347\pi$
$648$	−2.16176e6	+	746316.i	−0.202241	+	0.0698209i
$649$	−8.12237e6			−0.756957
$650$		0			0
$651$			7.00992e6i			0.648277i
$652$	2.63341e6	+	2.85403e6i	0.242605	+	0.262930i
$653$	−5.92231e6			−0.543511			−0.271755	−	0.962366i	$-0.587604\pi$
$653$	−5.92231e6			−0.543511			−0.271755	+	0.962366i	$0.587604\pi$
$654$	−1.36810e6	−	599166.i	−0.125076	−	0.0547776i
$655$		0			0
$656$	485615.	−	6.02943e6i	0.0440587	−	0.547037i
$657$		−	5.46793e6i		−	0.494208i
$658$	8.63333e6	−	1.97129e7i	0.777345	−	1.77495i
$659$			2.68146e6i			0.240523i	0.992742	+	0.120262i	$0.0383734\pi$
$659$			2.68146e6i			0.240523i	−0.992742	+	0.120262i	$0.961627\pi$
$660$		0			0
$661$		−	1.14098e7i		−	1.01572i	−0.861440	−	0.507859i	$-0.830437\pi$
$661$		−	1.14098e7i		−	1.01572i	0.861440	−	0.507859i	$-0.169563\pi$
$662$	−2.04394e6	−	895150.i	−0.181269	−	0.0793873i
$663$		−	2.92996e6i		−	0.258868i
$664$	1.14315e6	−	394657.i	0.100620	−	0.0347376i
$665$		0			0
$666$	3.04328e6	−	6.94887e6i	0.265862	−	0.607056i
$667$	−5.01481e6			−0.436456
$668$	1.31926e6	−	1.21728e6i	0.114390	−	0.105548i
$669$			3.02423e6i			0.261246i
$670$		0			0
$671$	1.25764e7			1.07833
$672$	−4.85921e6	+	9.04120e6i	−0.415090	+	0.772330i
$673$			5.13646e6i			0.437146i	0.975821	+	0.218573i	$0.0701402\pi$
$673$			5.13646e6i			0.437146i	−0.975821	+	0.218573i	$0.929860\pi$
$674$	7.09269e6	+	3.10627e6i	0.601397	+	0.263384i
$675$		0			0
$676$	7.70021e6	+	8.34533e6i	0.648091	+	0.702387i
$677$	−4.91407e6			−0.412068			−0.206034	−	0.978545i	$-0.566056\pi$
$677$	−4.91407e6			−0.412068			−0.206034	+	0.978545i	$0.566056\pi$
$678$	2.96804e6	+	1.29986e6i	0.247968	+	0.108598i
$679$	−2.44930e7			−2.03877
$680$		0			0
$681$	−6.41937e6			−0.530426
$682$	−6.59085e6	−	2.88648e6i	−0.542601	−	0.237634i
$683$	4.30841e6			0.353399			0.176700	−	0.984265i	$-0.443458\pi$
$683$	4.30841e6			0.353399			0.176700	+	0.984265i	$0.443458\pi$
$684$	4.30427e6	−	3.97154e6i	0.351770	−	0.324577i
$685$		0			0
$686$	−5.78043e6	−	2.53156e6i	−0.468975	−	0.205389i
$687$		−	1.00433e7i		−	0.811868i
$688$	−1.35146e6	+	1.67798e7i	−0.108851	+	1.35150i
$689$	3.92867e6			0.315281
$690$		0			0
$691$			2.17672e6i			0.173423i	0.996233	+	0.0867116i	$0.0276359\pi$
$691$			2.17672e6i			0.173423i	−0.996233	+	0.0867116i	$0.972364\pi$
$692$	−3.63837e6	−	3.94319e6i	−0.288829	−	0.313027i
$693$	−6.62361e6			−0.523916
$694$	−1.29211e6	+	2.95034e6i	−0.101836	+	0.232527i
$695$		0			0
$696$	−2.60442e6	−	7.54390e6i	−0.203792	−	0.590300i
$697$			1.24684e7i			0.972142i
$698$	−1.14025e7	−	4.99375e6i	−0.885851	−	0.387961i
$699$		−	1.18284e7i		−	0.915658i
$700$		0			0
$701$		−	1.31991e6i		−	0.101450i	−0.998713	−	0.0507248i	$-0.983847\pi$
$701$		−	1.31991e6i		−	0.101450i	0.998713	−	0.0507248i	$-0.0161531\pi$
$702$	1.16190e6	−	2.65303e6i	0.0889871	−	0.203189i
$703$		−	1.54987e7i		−	1.18279i
$704$	−6.49981e6	−	8.29162e6i	−0.494275	−	0.630533i
$705$		0			0
$706$	−1.30349e7	−	5.70870e6i	−0.984232	−	0.431048i
$707$	−1.87970e7			−1.41429
$708$	6.43081e6	−	5.93370e6i	0.482151	−	0.444879i
$709$		−	1.33410e7i		−	0.996721i	−0.866970	−	0.498360i	$-0.833936\pi$
$709$		−	1.33410e7i		−	0.996721i	0.866970	−	0.498360i	$-0.166064\pi$
$710$		0			0
$711$	−1.57885e6			−0.117130
$712$	1.54684e7	−	5.34024e6i	1.14353	−	0.394785i
$713$		−	4.87058e6i		−	0.358803i
$714$	8.48759e6	−	1.93801e7i	0.623073	−	1.42269i
$715$		0			0
$716$	−1.26039e7	+	1.16296e7i	−0.918800	+	0.847775i
$717$	−8.63721e6			−0.627445
$718$	−1.80369e6	+	4.11846e6i	−0.130573	+	0.298143i
$719$	−2.25289e7			−1.62524			−0.812620	−	0.582794i	$-0.801960\pi$
$719$	−2.25289e7			−1.62524			−0.812620	+	0.582794i	$0.801960\pi$
$720$		0			0
$721$	6.31691e6			0.452550
$722$	−819031.	+	1.87013e6i	−0.0584732	+	0.133515i
$723$	1.75199e7			1.24648
$724$	−2.66805e6	+	2.46180e6i	−0.189168	+	0.174545i
$725$		0			0
$726$	1.41671e6	−	3.23485e6i	0.0997562	−	0.227778i
$727$		−	1.49088e7i		−	1.04618i	−0.852277	−	0.523091i	$-0.824779\pi$
$727$		−	1.49088e7i		−	1.04618i	0.852277	−	0.523091i	$-0.175221\pi$
$728$	−1.24021e6	−	3.59237e6i	−0.0867296	−	0.251219i
$729$	1.20906e7			0.842617
$730$		0			0
$731$		−	3.46994e7i		−	2.40175i
$732$	−9.95727e6	+	9.18755e6i	−0.686851	+	0.633756i
$733$	7.98329e6			0.548810			0.274405	−	0.961614i	$-0.411519\pi$
$733$	7.98329e6			0.548810			0.274405	+	0.961614i	$0.411519\pi$
$734$	4.53037e6	+	1.98409e6i	0.310380	+	0.135932i
$735$		0			0
$736$	3.37624e6	−	6.28193e6i	0.229741	−	0.427463i
$737$		−	6.71802e6i		−	0.455588i
$738$	−1.68695e6	+	3.85190e6i	−0.114015	+	0.260336i
$739$			3.81018e6i			0.256646i	0.991732	+	0.128323i	$0.0409594\pi$
$739$			3.81018e6i			0.256646i	−0.991732	+	0.128323i	$0.959041\pi$
$740$		0			0
$741$		−	2.01885e6i		−	0.135070i
$742$	2.59861e7	+	1.13807e7i	1.73273	+	0.758855i
$743$		−	8.99457e6i		−	0.597734i	−0.954295	−	0.298867i	$-0.903391\pi$
$743$		−	8.99457e6i		−	0.597734i	0.954295	−	0.298867i	$-0.0966088\pi$
$744$	7.32693e6	−	2.52951e6i	0.485277	−	0.167535i
$745$		0			0
$746$	1.10337e7	−	2.51937e7i	0.725893	−	1.65747i
$747$	−840722.			−0.0551253
$748$	1.47266e7	+	1.59604e7i	0.962383	+	1.04301i
$749$			3.10156e7i			2.02011i
$750$		0			0
$751$	1.18325e7			0.765559			0.382779	−	0.923840i	$-0.374967\pi$
$751$	1.18325e7			0.765559			0.382779	+	0.923840i	$0.374967\pi$
$752$	−2.37197e7	−	1.91040e6i	−1.52955	−	0.123191i
$753$		−	4.86742e6i		−	0.312832i
$754$	2.70676e6	+	1.18543e6i	0.173389	+	0.0759362i
$755$		0			0
$756$	1.53708e7	−	1.41826e7i	0.978117	−	0.902506i
$757$	5.14086e6			0.326059			0.163030	−	0.986621i	$-0.447873\pi$
$757$	5.14086e6			0.326059			0.163030	+	0.986621i	$0.447873\pi$
$758$	6.43308e6	+	2.81739e6i	0.406673	+	0.178104i
$759$	−4.28467e6			−0.269968
$760$		0			0
$761$	8.21979e6			0.514516			0.257258	−	0.966343i	$-0.417181\pi$
$761$	8.21979e6			0.514516			0.257258	+	0.966343i	$0.417181\pi$
$762$	1.64699e7	+	7.21306e6i	1.02755	+	0.450020i
$763$	3.99322e6			0.248320
$764$	−8.50230e6	−	9.21461e6i	−0.526991	−	0.571142i
$765$		0			0
$766$	−160477.	−	70281.3i	−0.00988189	−	0.00432781i
$767$			3.23979e6i			0.198851i
$768$	1.12035e7	+	1.81646e6i	0.685410	+	0.111128i
$769$	1.11390e7			0.679251			0.339626	−	0.940561i	$-0.389700\pi$
$769$	1.11390e7			0.679251			0.339626	+	0.940561i	$0.389700\pi$
$770$		0			0
$771$		−	4.29101e6i		−	0.259970i
$772$	6.15030e6	−	5.67487e6i	0.371410	−	0.342699i
$773$	−5.63671e6			−0.339294			−0.169647	−	0.985505i	$-0.554263\pi$
$773$	−5.63671e6			−0.339294			−0.169647	+	0.985505i	$0.554263\pi$
$774$	4.69475e6	−	1.07198e7i	0.281683	−	0.643180i
$775$		0			0
$776$	8.83825e6	+	2.56007e7i	0.526880	+	1.52615i
$777$		−	1.88831e7i		−	1.12207i
$778$	2.21705e7	+	9.70963e6i	1.31318	+	0.575113i
$779$			8.59123e6i			0.507238i
$780$		0			0
$781$		−	4.46561e6i		−	0.261971i
$782$	−5.89728e6	+	1.34655e7i	−0.344854	+	0.787421i
$783$			1.62615e7i			0.947888i
$784$	821473.	−	1.01995e7i	0.0477313	−	0.592636i
$785$		0			0
$786$	−1.78209e7	−	7.80474e6i	−1.02890	−	0.450611i
$787$	−3.07197e7			−1.76799			−0.883996	−	0.467495i	$-0.845157\pi$
$787$	−3.07197e7			−1.76799			−0.883996	+	0.467495i	$0.845157\pi$
$788$	−1.95073e7	−	2.11416e7i	−1.11913	−	1.21289i
$789$			2.09361e7i			1.19730i
$790$		0			0
$791$	−8.66309e6			−0.492302
$792$	2.39011e6	+	6.92314e6i	0.135396	+	0.392184i
$793$		−	5.01639e6i		−	0.283275i
$794$	−5.24489e6	+	1.19759e7i	−0.295246	+	0.674151i
$795$		0			0
$796$	−1.81672e6	−	1.96892e6i	−0.101626	−	0.110140i
$797$	−2.22339e7			−1.23985			−0.619926	−	0.784660i	$-0.712837\pi$
$797$	−2.22339e7			−1.23985			−0.619926	+	0.784660i	$0.712837\pi$
$798$	5.84828e6	−	1.33537e7i	0.325103	−	0.742323i
$799$	4.90505e7			2.71817
$800$		0			0
$801$	−1.13761e7			−0.626488
$802$	−2.26106e6	+	5.16278e6i	−0.124130	+	0.283431i
$803$	1.39704e7			0.764577
$804$	4.90776e6	+	5.31893e6i	0.267759	+	0.290191i
$805$		0			0
$806$	−1.15134e6	+	2.62891e6i	−0.0624260	+	0.142540i
$807$		−	7.25226e6i		−	0.392003i
$808$	6.78285e6	+	1.96470e7i	0.365497	+	1.05869i
$809$	−1.51247e7			−0.812484			−0.406242	−	0.913765i	$-0.633161\pi$
$809$	−1.51247e7			−0.812484			−0.406242	+	0.913765i	$0.633161\pi$
$810$		0			0
$811$			1.35982e7i			0.725990i	0.931791	+	0.362995i	$0.118246\pi$
$811$			1.35982e7i			0.725990i	−0.931791	+	0.362995i	$0.881754\pi$
$812$	1.44698e7	+	1.56820e7i	0.770143	+	0.834665i
$813$	−2.26157e7			−1.20001
$814$	1.77542e7	+	7.77552e6i	0.939162	+	0.411309i
$815$		0			0
$816$	−2.33193e7	−	1.87815e6i	−1.22600	−	0.0987427i
$817$		−	2.39092e7i		−	1.25317i
$818$	−1.17540e7	+	2.68385e7i	−0.614191	+	1.40241i
$819$			2.64197e6i			0.137632i
$820$		0			0
$821$		−	2.56951e7i		−	1.33043i	−0.746651	−	0.665216i	$-0.768340\pi$
$821$		−	2.56951e7i		−	1.33043i	0.746651	−	0.665216i	$-0.231660\pi$
$822$	−9.10207e6	−	3.98628e6i	−0.469852	−	0.205773i
$823$		−	8.73184e6i		−	0.449372i	−0.974431	−	0.224686i	$-0.927864\pi$
$823$		−	8.73184e6i		−	0.449372i	0.974431	−	0.224686i	$-0.0721357\pi$
$824$	−2.27944e6	−	6.60257e6i	−0.116953	−	0.338762i
$825$		0			0
$826$	−9.38512e6	+	2.14295e7i	−0.478619	+	1.09285i
$827$	−1.46565e6			−0.0745191			−0.0372596	−	0.999306i	$-0.511863\pi$
$827$	−1.46565e6			−0.0745191			−0.0372596	+	0.999306i	$0.511863\pi$
$828$	−3.64372e6	+	3.36205e6i	−0.184701	+	0.170423i
$829$			4.49887e6i			0.227362i	0.993517	+	0.113681i	$0.0362641\pi$
$829$			4.49887e6i			0.227362i	−0.993517	+	0.113681i	$0.963736\pi$
$830$		0			0
$831$	8.97130e6			0.450664
$832$	−3.30729e6	+	2.59259e6i	−0.165640	+	0.129845i
$833$			2.10918e7i			1.05317i
$834$	−1.72052e7	−	7.53506e6i	−0.856532	−	0.375121i
$835$		0			0
$836$	1.01472e7	+	1.09973e7i	0.502146	+	0.544215i
$837$	−1.57938e7			−0.779244
$838$	−1.85349e7	−	8.11741e6i	−0.911758	−	0.399307i
$839$	1.43801e7			0.705273			0.352636	−	0.935760i	$-0.385285\pi$
$839$	1.43801e7			0.705273			0.352636	+	0.935760i	$0.385285\pi$
$840$		0			0
$841$	3.92030e6			0.191130
$842$	1.11846e7	+	4.89834e6i	0.543677	+	0.238105i
$843$	−2.59702e7			−1.25866
$844$	1.30206e7	−	1.20141e7i	0.629180	−	0.580543i
$845$		0			0
$846$	1.51533e7	+	6.63643e6i	0.727916	+	0.318793i
$847$			9.44185e6i			0.452219i
$848$	2.51834e6	−	3.12679e7i	0.120261	−	1.49317i
$849$	−2.17420e7			−1.03521
$850$		0			0
$851$			1.31202e7i			0.621036i
$852$	3.26230e6	+	3.53561e6i	0.153966	+	0.166865i
$853$	−2.62365e7			−1.23462			−0.617310	−	0.786720i	$-0.711778\pi$
$853$	−2.62365e7			−1.23462			−0.617310	+	0.786720i	$0.711778\pi$
$854$	1.45316e7	−	3.31808e7i	0.681820	−	1.55683i
$855$		0			0
$856$	3.24182e7	−	1.11919e7i	1.51218	−	0.522058i
$857$		−	6.34066e6i		−	0.294905i	−0.989069	−	0.147453i	$-0.952893\pi$
$857$		−	6.34066e6i		−	0.294905i	0.989069	−	0.147453i	$-0.0471074\pi$
$858$	2.31266e6	+	1.01284e6i	0.107249	+	0.0469701i
$859$			1.09488e7i			0.506273i	0.967431	+	0.253137i	$0.0814622\pi$
$859$			1.09488e7i			0.506273i	−0.967431	+	0.253137i	$0.918538\pi$
$860$		0			0
$861$			1.04673e7i			0.481200i
$862$	4.10501e6	−	9.37318e6i	0.188168	−	0.429654i
$863$			3.28604e6i			0.150192i	0.997176	+	0.0750958i	$0.0239263\pi$
$863$			3.28604e6i			0.150192i	−0.997176	+	0.0750958i	$0.976074\pi$
$864$	−2.03704e7	−	1.09481e7i	−0.928359	−	0.498948i
$865$		0			0
$866$	6.67978e6	+	2.92543e6i	0.302669	+	0.132555i
$867$	3.28540e7			1.48436
$868$	−1.52310e7	+	1.40536e7i	−0.686165	+	0.633123i
$869$		−	4.03393e6i		−	0.181209i
$870$		0			0
$871$	−2.67963e6			−0.119682
$872$	−1.44094e6	−	4.17380e6i	−0.0641735	−	0.185883i
$873$		−	1.88278e7i		−	0.836110i
$874$	−4.06345e6	+	9.27828e6i	−0.179936	+	0.410855i
$875$		0			0
$876$	−1.10610e7	+	1.02059e7i	−0.487005	+	0.449358i
$877$	−7.75326e6			−0.340397			−0.170198	−	0.985410i	$-0.554441\pi$
$877$	−7.75326e6			−0.340397			−0.170198	+	0.985410i	$0.554441\pi$
$878$	4.30481e6	−	9.82937e6i	0.188459	−	0.430318i
$879$	−1.88557e7			−0.823136
$880$		0			0
$881$	−449453.			−0.0195094			−0.00975471	−	0.999952i	$-0.503105\pi$
$881$	−449453.			−0.0195094			−0.00975471	+	0.999952i	$0.503105\pi$
$882$	−2.85367e6	+	6.51592e6i	−0.123519	+	0.282036i
$883$	−2.42001e7			−1.04452			−0.522259	−	0.852787i	$-0.674911\pi$
$883$	−2.42001e7			−1.04452			−0.522259	+	0.852787i	$0.674911\pi$
$884$	6.36614e6	−	5.87402e6i	0.273997	−	0.252816i
$885$		0			0
$886$	−1.36610e7	+	3.11928e7i	−0.584652	+	1.33496i
$887$			8.80204e6i			0.375642i	0.982203	+	0.187821i	$0.0601425\pi$
$887$			8.80204e6i			0.375642i	−0.982203	+	0.187821i	$0.939857\pi$
$888$	−1.97370e7	+	6.81392e6i	−0.839943	+	0.289978i
$889$	−4.80724e7			−2.04005
$890$		0			0
$891$			4.06203e6i			0.171415i
$892$	−6.57097e6	+	6.06302e6i	−0.276514	+	0.255139i
$893$	3.37977e7			1.41827
$894$	−2.06460e7	−	9.04197e6i	−0.863956	−	0.378372i
$895$		0			0
$896$	−2.93863e7	+	7.56797e6i	−1.22286	+	0.314926i
$897$			1.70903e6i			0.0709202i
$898$	−5.44826e6	+	1.24403e7i	−0.225459	+	0.514801i
$899$		−	1.61137e7i		−	0.664959i
$900$		0			0
$901$			6.46597e7i			2.65352i
$902$	−9.84151e6	−	4.31012e6i	−0.402759	−	0.176390i
$903$		−	2.91302e7i		−	1.18884i
$904$	3.12606e6	+	9.05486e6i	0.127226	+	0.368520i
$905$		0			0
$906$	8.27351e6	−	1.88913e7i	0.334865	−	0.764613i
$907$	1.35035e7			0.545040			0.272520	−	0.962150i	$-0.412143\pi$
$907$	1.35035e7			0.545040			0.272520	+	0.962150i	$0.412143\pi$
$908$	−1.28697e7	−	1.39479e7i	−0.518027	−	0.561426i
$909$		−	1.44492e7i		−	0.580010i
$910$		0			0
$911$	−1.74802e7			−0.697831			−0.348915	−	0.937154i	$-0.613450\pi$
$911$	−1.74802e7			−0.697831			−0.348915	+	0.937154i	$0.613450\pi$
$912$	−1.60679e7	−	1.29412e6i	−0.639693	−	0.0515213i
$913$		−	2.14803e6i		−	0.0852830i
$914$	4.45083e6	+	1.94926e6i	0.176228	+	0.0771798i
$915$		0			0
$916$	2.18219e7	−	2.01350e7i	0.859317	−	0.792890i
$917$	5.20157e7			2.04273
$918$	4.36647e7	+	1.91231e7i	1.71011	+	0.748948i
$919$	−3.84416e7			−1.50146			−0.750728	−	0.660612i	$-0.770297\pi$
$919$	−3.84416e7			−1.50146			−0.750728	+	0.660612i	$0.770297\pi$
$920$		0			0
$921$	−1.05934e7			−0.411514
$922$	1.20983e7	+	5.29849e6i	0.468702	+	0.205270i
$923$	−1.78121e6			−0.0688194
$924$	1.23630e7	+	1.33988e7i	0.476370	+	0.516280i
$925$		0			0
$926$	−7.00542e6	−	3.06805e6i	−0.268477	−	0.117580i
$927$			4.85580e6i			0.185593i
$928$	1.11698e7	−	2.07830e7i	0.425772	−	0.792205i
$929$	694053.			0.0263848			0.0131924	−	0.999913i	$-0.495801\pi$
$929$	694053.			0.0263848			0.0131924	+	0.999913i	$0.495801\pi$
$930$		0			0
$931$			1.45330e7i			0.549518i
$932$	2.57005e7	−	2.37138e7i	0.969174	−	0.894254i
$933$	1.70643e7			0.641776
$934$	−1.46149e7	+	3.33709e7i	−0.548186	+	1.25170i
$935$		0			0
$936$	2.76145e6	−	953349.i	0.103026	−	0.0355682i
$937$			4.08849e7i			1.52130i	0.649165	+	0.760648i	$0.275119\pi$
$937$			4.08849e7i			1.52130i	−0.649165	+	0.760648i	$0.724881\pi$
$938$	−1.77243e7	−	7.76244e6i	−0.657753	−	0.288065i
$939$			1.74225e7i			0.644832i
$940$		0			0
$941$		−	1.21324e7i		−	0.446655i	−0.974743	−	0.223328i	$-0.928308\pi$
$941$		−	1.21324e7i		−	0.446655i	0.974743	−	0.223328i	$-0.0716920\pi$
$942$	−6.66289e6	+	1.52137e7i	−0.244645	+	0.558609i
$943$		−	7.27279e6i		−	0.266331i
$944$	2.57852e7	+	2.07676e6i	0.941760	+	0.0758500i
$945$		0			0
$946$	2.73887e7	+	1.19950e7i	0.995049	+	0.435785i
$947$	−3.38948e7			−1.22817			−0.614084	−	0.789241i	$-0.710474\pi$
$947$	−3.38948e7			−1.22817			−0.614084	+	0.789241i	$0.710474\pi$
$948$	2.94694e6	+	3.19383e6i	0.106500	+	0.115422i
$949$		−	5.57242e6i		−	0.200853i
$950$		0			0
$951$	1.63086e7			0.584742
$952$	5.91247e7	−	2.04119e7i	2.11435	−	0.729948i
$953$			5.18152e7i			1.84810i	0.382274	+	0.924049i	$0.375141\pi$
$953$			5.18152e7i			1.84810i	−0.382274	+	0.924049i	$0.624859\pi$
$954$	−8.74833e6	+	1.99755e7i	−0.311210	+	0.710602i
$955$		0			0
$956$	−1.73160e7	−	1.87667e7i	−0.612778	−	0.664116i
$957$	−1.41753e7			−0.500324
$958$	−4.20641e6	+	9.60470e6i	−0.148080	+	0.338119i
$959$	2.65671e7			0.932819
$960$		0			0
$961$	−1.29789e7			−0.453347
$962$	3.10144e6	−	7.08166e6i	0.108050	−	0.246716i
$963$	−2.38416e7			−0.828458
$964$	3.51241e7	+	3.80667e7i	1.21734	+	1.31933i
$965$		0			0
$966$	−4.95078e6	+	1.13044e7i	−0.170699	+	0.389765i
$967$		−	4.41440e7i		−	1.51812i	−0.651023	−	0.759058i	$-0.725660\pi$
$967$		−	4.41440e7i		−	1.51812i	0.651023	−	0.759058i	$-0.274340\pi$
$968$	9.86884e6	−	3.40707e6i	0.338515	−	0.116867i
$969$	3.32272e7			1.13680
$970$		0			0
$971$		−	2.25369e7i		−	0.767091i	−0.923522	−	0.383546i	$-0.874703\pi$
$971$		−	2.25369e7i		−	0.767091i	0.923522	−	0.383546i	$-0.125297\pi$
$972$	1.80847e7	+	1.95998e7i	0.613967	+	0.665404i
$973$	5.02184e7			1.70052
$974$	−1.30407e7	−	5.71122e6i	−0.440457	−	0.192900i
$975$		0			0
$976$	−3.99250e7	−	3.21558e6i	−1.34159	−	0.108053i
$977$		−	508955.i		−	0.0170586i	−0.999964	−	0.00852929i	$-0.997285\pi$
$977$		−	508955.i		−	0.0170586i	0.999964	−	0.00852929i	$-0.00271499\pi$
$978$	−2.98088e6	+	6.80639e6i	−0.0996546	+	0.227546i
$979$		−	2.90657e7i		−	0.969224i
$980$		0			0
$981$			3.06958e6i			0.101837i
$982$	−2.79354e7	−	1.22344e7i	−0.924433	−	0.404859i
$983$			1.38312e7i			0.456536i	0.973598	+	0.228268i	$0.0733063\pi$
$983$			1.38312e7i			0.456536i	−0.973598	+	0.228268i	$0.926694\pi$
$984$	1.09406e7	−	3.77709e6i	0.360209	−	0.124357i
$985$		0			0
$986$	−1.95104e7	+	4.45490e7i	−0.639107	+	1.45930i
$987$	4.11781e7			1.34547
$988$	4.38652e6	−	4.04743e6i	0.142964	−	0.131913i
$989$			2.02400e7i			0.657992i
$990$		0			0
$991$	1.13368e7			0.366696			0.183348	−	0.983048i	$-0.441307\pi$
$991$	1.13368e7			0.366696			0.183348	+	0.983048i	$0.441307\pi$
$992$	2.01852e7	+	1.08486e7i	0.651259	+	0.350020i
$993$		−	4.26957e6i		−	0.137408i
$994$	−1.17818e7	−	5.15986e6i	−0.378220	−	0.165643i
$995$		0			0
$996$	1.56921e6	+	1.70068e6i	0.0501226	+	0.0543218i
$997$	−3.66390e7			−1.16736			−0.583681	−	0.811983i	$-0.698388\pi$
$997$	−3.66390e7			−1.16736			−0.583681	+	0.811983i	$0.698388\pi$
$998$	−1.64964e7	−	7.22464e6i	−0.524278	−	0.229609i
$999$	4.25449e7			1.34876

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.b.149.8		20
4.3	odd	2		800.6.f.c.49.13		20
5.2	odd	4		200.6.d.b.101.3		20
5.3	odd	4		40.6.d.a.21.18	yes	20
5.4	even	2		200.6.f.c.149.13		20
8.3	odd	2		800.6.f.b.49.7		20
8.5	even	2		200.6.f.c.149.14		20
15.8	even	4		360.6.k.b.181.3		20
20.3	even	4		160.6.d.a.81.14		20
20.7	even	4		800.6.d.c.401.7		20
20.19	odd	2		800.6.f.b.49.8		20
40.3	even	4		160.6.d.a.81.7		20
40.13	odd	4		40.6.d.a.21.17	✓	20
40.19	odd	2		800.6.f.c.49.14		20
40.27	even	4		800.6.d.c.401.14		20
40.29	even	2	inner	200.6.f.b.149.7		20
40.37	odd	4		200.6.d.b.101.4		20
120.53	even	4		360.6.k.b.181.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.17	✓	20	40.13	odd	4
40.6.d.a.21.18	yes	20	5.3	odd	4
160.6.d.a.81.7		20	40.3	even	4
160.6.d.a.81.14		20	20.3	even	4
200.6.d.b.101.3		20	5.2	odd	4
200.6.d.b.101.4		20	40.37	odd	4
200.6.f.b.149.7		20	40.29	even	2	inner
200.6.f.b.149.8		20	1.1	even	1	trivial
200.6.f.c.149.13		20	5.4	even	2
200.6.f.c.149.14		20	8.5	even	2
360.6.k.b.181.3		20	15.8	even	4
360.6.k.b.181.4		20	120.53	even	4
800.6.d.c.401.7		20	20.7	even	4
800.6.d.c.401.14		20	40.27	even	4
800.6.f.b.49.7		20	8.3	odd	2
800.6.f.b.49.8		20	20.19	odd	2
800.6.f.c.49.13		20	4.3	odd	2
800.6.f.c.49.14		20	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.26935 + 5.18171i) q^{2} -10.8240 q^{3} +(-21.7001 - 23.5182i) q^{4} +(24.5634 - 56.0868i) q^{6} +163.706i q^{7} +(171.109 - 59.0729i) q^{8} -125.841 q^{9} +O(q^{10})\)	\(q+(-2.26935 + 5.18171i) q^{2} -10.8240 q^{3} +(-21.7001 - 23.5182i) q^{4} +(24.5634 - 56.0868i) q^{6} +163.706i q^{7} +(171.109 - 59.0729i) q^{8} -125.841 q^{9} -321.520i q^{11} +(234.883 + 254.561i) q^{12} -128.246 q^{13} +(-848.277 - 371.506i) q^{14} +(-82.2074 + 1020.69i) q^{16} -2110.72i q^{17} +(285.576 - 652.070i) q^{18} -1454.37i q^{19} -1771.96i q^{21} +(1666.02 + 729.641i) q^{22} +1231.18i q^{23} +(-1852.09 + 639.406i) q^{24} +(291.033 - 664.531i) q^{26} +3992.34 q^{27} +(3850.07 - 3552.45i) q^{28} +4073.19i q^{29} -3956.03 q^{31} +(-5102.38 - 2742.28i) q^{32} +3480.14i q^{33} +(10937.1 + 4789.95i) q^{34} +(2730.76 + 2959.54i) q^{36} +10656.6 q^{37} +(7536.11 + 3300.46i) q^{38} +1388.13 q^{39} -5907.19 q^{41} +(9181.76 + 4021.18i) q^{42} +16439.6 q^{43} +(-7561.57 + 6977.04i) q^{44} +(-6379.59 - 2793.96i) q^{46} +23238.8i q^{47} +(889.814 - 11048.0i) q^{48} -9992.68 q^{49} +22846.5i q^{51} +(2782.95 + 3016.10i) q^{52} -30634.0 q^{53} +(-9059.99 + 20687.1i) q^{54} +(9670.60 + 28011.6i) q^{56} +15742.1i q^{57} +(-21106.1 - 9243.47i) q^{58} -25262.4i q^{59} +39115.5i q^{61} +(8977.61 - 20499.0i) q^{62} -20600.9i q^{63} +(25788.8 - 20215.9i) q^{64} +(-18033.1 - 7897.64i) q^{66} +20894.5 q^{67} +(-49640.3 + 45803.0i) q^{68} -13326.3i q^{69} +13889.1 q^{71} +(-21532.5 + 7433.78i) q^{72} +43451.2i q^{73} +(-24183.6 + 55219.6i) q^{74} +(-34204.1 + 31560.0i) q^{76} +52634.8 q^{77} +(-3150.15 + 7192.89i) q^{78} +12546.4 q^{79} -12633.8 q^{81} +(13405.4 - 30609.3i) q^{82} +6680.84 q^{83} +(-41673.2 + 38451.7i) q^{84} +(-37307.1 + 85185.1i) q^{86} -44088.2i q^{87} +(-18993.2 - 55015.1i) q^{88} +90400.9 q^{89} -20994.6i q^{91} +(28955.0 - 26716.7i) q^{92} +42820.2 q^{93} +(-120416. - 52736.8i) q^{94} +(55228.3 + 29682.5i) q^{96} +149616. i q^{97} +(22676.8 - 51779.1i) q^{98} +40460.4i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 - 36 * q^3 + 32 * q^4 + 204 * q^6 - 248 * q^8 + 1620 * q^9	\( 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9} - 1252 q^{12} - 2708 q^{14} + 3080 q^{16} - 2070 q^{18} - 8244 q^{22} - 1032 q^{24} - 8084 q^{26} - 11664 q^{27} - 22924 q^{28} + 7160 q^{31} - 14792 q^{32} - 21132 q^{34} + 18344 q^{36} + 3608 q^{37} + 16884 q^{38} + 44904 q^{39} + 11608 q^{41} + 49444 q^{42} + 51772 q^{43} - 72296 q^{44} - 28516 q^{46} + 85048 q^{48} - 18756 q^{49} + 111624 q^{52} - 928 q^{53} + 100584 q^{54} - 53624 q^{56} - 152344 q^{58} - 228648 q^{62} + 11264 q^{64} - 56688 q^{66} + 161604 q^{67} - 359040 q^{68} - 200312 q^{71} - 563448 q^{72} - 78876 q^{74} - 153872 q^{76} - 26008 q^{77} + 624640 q^{78} - 282080 q^{79} + 65172 q^{81} + 410576 q^{82} + 99092 q^{83} + 297128 q^{84} + 27452 q^{86} + 464496 q^{88} + 3160 q^{89} + 519244 q^{92} - 293472 q^{93} - 148820 q^{94} + 395168 q^{96} - 663674 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 36 * q^3 + 32 * q^4 + 204 * q^6 - 248 * q^8 + 1620 * q^9 - 1252 * q^12 - 2708 * q^14 + 3080 * q^16 - 2070 * q^18 - 8244 * q^22 - 1032 * q^24 - 8084 * q^26 - 11664 * q^27 - 22924 * q^28 + 7160 * q^31 - 14792 * q^32 - 21132 * q^34 + 18344 * q^36 + 3608 * q^37 + 16884 * q^38 + 44904 * q^39 + 11608 * q^41 + 49444 * q^42 + 51772 * q^43 - 72296 * q^44 - 28516 * q^46 + 85048 * q^48 - 18756 * q^49 + 111624 * q^52 - 928 * q^53 + 100584 * q^54 - 53624 * q^56 - 152344 * q^58 - 228648 * q^62 + 11264 * q^64 - 56688 * q^66 + 161604 * q^67 - 359040 * q^68 - 200312 * q^71 - 563448 * q^72 - 78876 * q^74 - 153872 * q^76 - 26008 * q^77 + 624640 * q^78 - 282080 * q^79 + 65172 * q^81 + 410576 * q^82 + 99092 * q^83 + 297128 * q^84 + 27452 * q^86 + 464496 * q^88 + 3160 * q^89 + 519244 * q^92 - 293472 * q^93 - 148820 * q^94 + 395168 * q^96 - 663674 * q^98

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